Problem: Roger gets $\$40$ per day as wages and $\$4.50$ as commission for every pair of shoes he sells in a day. His daily earnings goal is $\$112$. Write an equation to determine how many pairs of shoes, $p$, Roger must sell in a day to meet his daily earnings goal. Find the number of pairs of shoes he must sell to meet his daily earnings goal.
Answer: Let $p$ be the number of shoes Roger has to sell to meet his daily earnings goal. Roger is paid $\$40$ in wages per day. His commission for selling $p$ pairs of shoes is $\$4.50p$. His total earnings for the day is $40+4.5p$. Since his earnings goal $\$112$, let's set this equal to $112$ : $ 40+4.50p=112$ Now, let's solve the equation to find the number of pairs of shoes $(p)$ Roger has to sell to meet his daily earnings goal. $\begin{aligned} 40+4.5p&=112\\ \\ 40+4.5p{-40}&=112{-40}&&{\text{subtract }40} \text{ from each side}\\ \\ 4.5p&=72\\ \\ \dfrac{4.5p}{{4.5}}&=\dfrac{72}{{4.5}}&&\text{divide each side by ${4.5}$}\\ \\ p&=16\end{aligned}$ The equation is $40+4.5p=112$. Roger must sell $16$ pairs of shoes to meet his daily earnings goal.